Question

In matlab please

3. (15 Points) Consider the following function. f(t) = 5e(-31) cos(20) a. Plot the function for t = 0 to 1 b. Analytically calculate the derivative. C. Calculate the derivative using the diff function d. Calculate the derivative using the gradient function e. In a separate figure, plot the derivatives obtained above in a single new figure (not subplot) using (i) solid blue line for part b, (ii) red dots for part c, and (iii) green o's for part d.

Answer 1

Analytical f'(t)= 5cos(20+)*(-3el-31) 1+5e-34) (-20sin ( 20t)) f'(t)=-15cos (20t )el-31) – 100 sin (20t)e (-31)

Function 5 4 3 2 f(t) -1 -2 نیا 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 t

Derivative by Analytical 60 40 20 df(t)/dt -20 우 -60 -80 -100 0.1 0.2. 0.3 0.4 0.5 0.6 0.7 100 0.9 t

Derivative by Diff function 60 40 20 df(t)/dt -20 -40 -60 -80 -100 0.1 0.2. 0.3 0.4 0.5 0.6 0.7 100 0.9 t

Derivative by gradient function 60 40 0 20 0 0 0 df(t)/dt -20 0 40 O 2 -60 -80 -100 0 0.1 0.2. 0.3 0.4 0.5 0.6 0.7 100 0.9 t

clc;clear all;close all
t1=0:0.01:1;
F=5*exp(-3*t1).*cos(20*t1);%Function
F1=-(15.*cos(20*t1).*exp(-3*t1))-(100.*sin(20*t1).*exp(-3*t1));%Analytical derivative
syms t
f=5*exp(-3*t).*cos(20*t);%Function
f2=diff(f);
t1=0:0.01:1;
F2=vpa(subs(f2,t,t1));
f3=gradient(f,t);
F3=vpa(subs(f3,t,t1));

figure
plot(t1,F)
xlabel('t')
ylabel('f(t)')
title('Function')

figure
plot(t1,F1,'color','b')
xlabel('t')
ylabel('df(t)/dt')
title('Derivative by Analytical')

figure
plot(t1,F2,'.','color','r')
xlabel('t')
ylabel('df(t)/dt')
title('Derivative by Diff function')

figure
plot(t1,F1,'o','color','g')
xlabel('t')
ylabel('df(t)/dt')
title('Derivative by gradient function')